This invention relates to X-ray imaging techniques, and, more particularly, to computerized tomography X-ray imaging using a minimal set of cone beam data measurements.
Computerized tomography (CT) uses a source of imaging energy such as X-ray energy and a detector for detecting imaging energy that has passed through an object of interest, often a patient being imaged for medical purposes. Typically, a single point source is used with an area detector such as an X-ray detector array.
Relative movement between the source, object of interest, and detector is used to collect data for image reconstruction purposes. Usually the source is moved, while the object and detector remain stationary relative to each other.
Typical source trajectories are "1 dimensional manifolds" described by parametric equations of a single variable. The advent of area X-ray detectors permits measurement of a 2 dimensional data set for each source position, since the detector lies in a 2 dimensional plane. Therefore, it is possible to measure a 1+2=3 dimensional data set of line integrals of the object being imaged.
This dimensional count is encouraging for volumetric imaging such as CT because the imaging object lies in three spatial dimensions. More specifically, complete CT data for a family of parallel planes constitutes a 2+1=3 dimensional data set and completely determines the imaging object.
Unfortunately, cone beam data generated by a single point source does not permit such simple reconstruction. A single circular trajectory does not provide a complete data set for Radon reconstruction (i.e., apart from measurement and discretization errors). Therefore, various scan trajectories have been used.
Among scan trajectories are those disclosed in U.S. Pat. No. 5,465,283 issued Nov. 7, 1995 to Tam. That patent discloses, among other information, the use of a scan trajectory of two offset circular scans with a line extending between them.
Generally, the scan trajectories result from relative movement among the source, detector, and object being imaged. Usually, the source is moved in a path about the object to define the scan trajectory. The object being imaged is often a medical patient, but could also be an industrial part being imaged to locate possible defects. When the object being imaged is an industrial part, the scan trajectory may be defined at least partly by movement of the object relative to the source and/or relative to the detector. A scan trajectory might also be defined at least partly by movement of the detector.
Such scan trajectories that provide complete cone beam data may present a number of problems. The path or paths followed by the source or other component being moved may be complex. This requires a complex robotic function. Additionally, the scan time for obtaining a complete data set may be longer than desirable. Especially in the case where the imaged object is a patient, it is desirable to limit the time and dose of X-ray exposure. A complex scan path requires a longer time of exposure than a simple path. Yet, if the dose is reduced to partially compensate for a long exposure time, the signal to noise ratio is reduced. Errors in the data, particularly due to lag and signal to noise degradation with decreasing dose, often are more troublesome with complex scan paths. Further, a complex scan path increases the amount of measured data and this in turn increases computational demands when using the reconstruction process to provide an image.
Although it is possible to provide image reconstruction with a incomplete data set, such a reconstructed image will be quite inexact, if not undetermined, in some regions as a result of not having the missing data.